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Simplifying (4 + 8i)(10 + -5i) = 0 Multiply (4 + 8i) * (10 + -5i) (4(10 + -5i) + 8i * (10 + -5i)) = 0 ((10 * 4 + -5i * 4) + 8i * (10 + -5i)) = 0 ((40 + -20i) + 8i * (10 + -5i)) = 0 (40 + -20i + (10 * 8i + -5i * 8i)) = 0 (40 + -20i + (80i + -40i2)) = 0 Combine like terms: -20i + 80i = 60i (40 + 60i + -40i2) = 0 Solving 40 + 60i + -40i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '20'. 20(2 + 3i + -2i2) = 0 Factor a trinomial. 20((2 + -1i)(1 + 2i)) = 0 Ignore the factor 20.Subproblem 1
Set the factor '(2 + -1i)' equal to zero and attempt to solve: Simplifying 2 + -1i = 0 Solving 2 + -1i = 0 Move all terms containing i to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1i = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1i = 0 + -2 -1i = 0 + -2 Combine like terms: 0 + -2 = -2 -1i = -2 Divide each side by '-1'. i = 2 Simplifying i = 2Subproblem 2
Set the factor '(1 + 2i)' equal to zero and attempt to solve: Simplifying 1 + 2i = 0 Solving 1 + 2i = 0 Move all terms containing i to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 2i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2i = 0 + -1 2i = 0 + -1 Combine like terms: 0 + -1 = -1 2i = -1 Divide each side by '2'. i = -0.5 Simplifying i = -0.5Solution
i = {2, -0.5}
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